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A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is

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Question: A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?

Options:

  1. 15 m²
  2. 7.5 m²
  3. 3.75 m²
  4. 1.5 m²

Correct Answer: 7.5 m²

Solution: 

Maximum error in area = 2 * length * uncertainty = 2 * 15.0 * 0.5 = 15 m².

A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is

Practice Questions

Q1
A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
  1. 15 m²
  2. 7.5 m²
  3. 3.75 m²
  4. 1.5 m²

Questions & Step-by-Step Solutions

A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
  • Step 1: Understand that the length of the rectangle is given as 15.0 m.
  • Step 2: Note that there is an uncertainty in the length measurement, which is ±0.5 m.
  • Step 3: Recognize that the area of a rectangle is calculated using the formula: Area = length × width.
  • Step 4: Since we are only given one length and no width, we will assume the width is also the same as the length for this calculation.
  • Step 5: Calculate the maximum possible error in the area using the formula: Maximum error in area = 2 × length × uncertainty.
  • Step 6: Substitute the values into the formula: Maximum error in area = 2 × 15.0 m × 0.5 m.
  • Step 7: Perform the multiplication: 2 × 15.0 = 30.0 and then 30.0 × 0.5 = 15.0.
  • Step 8: Conclude that the maximum possible error in the area calculation is 15 m².
  • Measurement Uncertainty – Understanding how uncertainty in measurements affects calculated values, particularly in area calculations.
  • Area Calculation – Applying the formula for the area of a rectangle and understanding how to incorporate uncertainties in the dimensions.
  • Propagation of Uncertainty – Using the correct method to propagate uncertainties when performing calculations involving multiple variables.
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